animate pixels (time series) of a raster
You can use your images as an image sequence in Blender.

If the names of the images files are like this :


You can setup this image sequence for the displacement modifier (like in the tutorial of your question).

Simply, use these parameters in the texture panel :


1 : indicate here the first image
2 : set the image sequence option
3 : indicate the number of frames you need




Now to animate you can or use Alt + A (Esc to stop), or open a timeline view and move it manually.



Note : your second approach let think about "shape keys", but a shape key only allows to interpolate between 2 shapes of the mesh and not through the several steps you need (or there is something I don't know).